Hawking Radiation Of Nonstationary Black Holes And Exact Solutions To Scalar Field Equation

Ever since Hawking discovered in 1974 that a black hole is not completely black but can emit radiation from its event horizon, considerable efforts had been made to reveal the quantum thermal properties of various kinds of black holes by many different methods in the past quarter century. However, most of these researches were concentrated on studying the thermal effect of static or stationary black holes. Because a realistic black hole in astrophysics can radiate or absorb matter surrounding it, it is non-stationary and evolves in the time. Thus the studies of the thermal properties of non-stationary black holes are more meaningful than that of stationary ones. But there are very limited tools to deal with the Hawking evaporation of non-stationary black holes. The traditionary method by calculating the renormalized energy momentum tensor can be used only in the spherical symmetric case, and it deals with the problem in an approximate manner. Thus this method is of limited use and meets great difficulties in other most general cases.The method of generalized tortoise coordinate transformation (GTCT) suggested by Prof. Zhao Zheng is, however, very different from that one. It has been used successfully to investigate the thermal properties of all kinds of black hole space-times. Prior to our work, as to the best of our knowledge, this method still has some difficulties in dealing with the Hawking evaporation of Dirac particles in the non-stationary Kerr(-Newman) black holes and in the accelerating Kinnersley space-tunes. The aim of this thesis is to settle down this problem, to develop the GTCT method further, and to make it become a fairly integrated system so that it can be used to tackle with the thermal effect of particles with arbitrary spins in the most general space-times.The main topic of this thesis is to investigate the behaviors of quantum fields in all specific black hole space-times. It can be divided into two parts: one is to find exact solutions to miscellaneous wave equations of quantum fields such asKlein-Gordon scalar field on some known black hole background geometries. The other is to discuss the thermal effect of quantum fields in various kinds of black hole space-times, focusing on the Hawking radiation of Dirac particles in the non-stationary black holes. It should be noted that here we only concern about the four dimensional case, neglecting other dimensional black holes. This dissertation has nine chapters.Chapter 1 introduces concisely some essential black hole theories with relation to this dissertation, including a brief history of the developments of black hole physics, classification of four dimensional black hole space-times, classical processes and quantum effects near black hole event horizon and four laws of black hole thermodynamics.In Chapter 2, we study exact solutions of the separated parts of Klein-Gordon field equation on some stationary and axisymmetry black hole backgrounds. We demonstrate that the radial and angular parts of a massive scalar field equation in the Kerr-Newman and Kerr-Sen black hole space-tunes satisfies the generalized spheroidal wave equation which is, in fact, a confluent Heun equation. On the base of the Laplace transformation, we present a new set of integral equations that relate two solutions with different parameters. Analogically, it can be generally shown that perturbations of massless fields with arbitrary spins in the Plebanski-Demianski metric (space-time of Petrov D-type) satisfy the generalized Teukolsky equation and their separated parts can be transformed into the form of Heun equation.In the third chapter, we first review the history backgrounds about the discovery of Hawking effect, and explain the physical mechanism that leads to black hole radiation. Then we introduce various methods that can deduce Hawking radiation, some recent researches on this theory and possible experimental ansatz that may test Hawking radiation.Chapter 4 emphasizes the Damour-Ruffini-Sannan (DRS) method and apply it to discuss the Hawking e...